8x(x-1)=(2x+9)(x-1)

Solution for 8x(x-1)=(2x+9)(x-1) equation:

8x(x-1)=(2x+9)(x-1)

We move all terms to the left:

8x(x-1)-((2x+9)(x-1))=0

We multiply parentheses

8x^2-8x-((2x+9)(x-1))=0

We multiply parentheses ..

8x^2-((+2x^2-2x+9x-9))-8x=0


We calculate terms in parentheses: -((+2x^2-2x+9x-9)), so:

(+2x^2-2x+9x-9)

We get rid of parentheses

2x^2-2x+9x-9

We add all the numbers together, and all the variables

2x^2+7x-9

Back to the equation:

-(2x^2+7x-9)


We add all the numbers together, and all the variables

8x^2-8x-(2x^2+7x-9)=0

We get rid of parentheses

8x^2-2x^2-8x-7x+9=0

We add all the numbers together, and all the variables

6x^2-15x+9=0

a = 6; b = -15; c = +9;
Δ = b2-4ac
Δ = -152-4·6·9
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3}{2*6}=\frac{12}{12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3}{2*6}=\frac{18}{12}
=1+1/2
$